A theoretical probe into the separation of CO2/CH4/N2 mixtures with polysulfone/polydimethylsiloxane–nano zinc oxide MMM

In the current investigation, molecular dynamics (MD) and Grand Canonical Monte Carlo (GCMC) simulation as remarkable and competent approaches have been employed for understanding structural and transport properties of MMMs in the realm of gas separation. The two commonly used polymers i.e. polysulfone (Psf) and polydimethylsiloxane (PDMS) as well as zinc oxide (ZnO) nanoparticle (NP) were used to carefully examine the transport properties of three light gasses (CO2, N2 and CH4) through simple Psf, Psf/PDMS composite loaded by different amounts of ZnO NP. Also, the fractional free volume (FFV), X-ray diffraction (XRD), glass transition temperature (Tg), and Equilibrium density were calculated to scrutinize the structural characterizations of the membranes. Moreover, the effect of feed pressure (4–16 bar) on gas separation performance of simulated MMMs was investigated. Results obtained in different experiments showed a clear improvement in the performance of simulated membranes by adding PDMS to PSf matrix. The selectivity of studied MMMs was in the range from 50.91 to 63.05 at pressures varying from 4 to 16 bar for the CO2/N2 gas pair, whereas the corresponding value for CO2/CH4 system was found to be in the range 27.27–46.24. For 6 wt% ZnO in 80%PSf + 20%PDMS membrane, high permeabilities of 78.02, 2.86 and 1.33 barrers were observed for CO2, CH4 and N2 gases, respectively. The 90%PSf + 10%PDMS membrane with 2% ZnO had a highest CO2/N2 selectivity value of 63.05 and its CO2 permeability at 8 bar was 57 barrer.

www.nature.com/scientificreports/ MMMs. Transport properties of three different gas molecules (CO 2 , CH 4 and N 2 ) through the simulated MMMs have been well investigated and discussed. Herein, surface topography, morphology, sorption and diffusion of gas molecules, the membrane crystallinity, and other structural and transport properties of this MMM have been studied. Furthermore, all the simulation results have been extracted and compared with experimental result to examine the reliability of current simulation which is proven that both results are consistent in approach.

Simulation theory
Force field. A force field consists of a series of potential functions and numerical parameters to explain the interaction potential. In the past, a number of these power fields have been developed for a variety of systems. For example, the force field of the Molecular Mechanics (MM) force field can be used for organic compounds, free radicals, and ions 54 . Another force field called AMBER is suitable for proteins, nucleic acids and polysaccharides 55 . Moreover, there are some promising, comprehensive and more complicated force fields which can be used to measure complex properties of materials like molecular structure, spectrum, and adaptations. These parameters have been obtained using a combination of mechanical quantum computing and laboratory data. PCFF, CVFF, Deriding, Universal, and COMPASS are the main and the most commonly used force field. In present article, the COMPASS force field has been utilized not just because of covering all the molecular interactions, but because COMPASS is a promising force field that supports atomistic simulations of condensed phase materials and represent the state-of-the-art force field technology 56 . COMPASS force field is able to predict the properties of a broad range of systems with high accuracy. Its main aim is to estimate the molecular properties, with an accuracy comparable with experiment 44 .

Materials used. The investigation utilized molecular dynamics (MD) and Monte Carlo simulation tech-
niques to create mixed matrix membranes (MMMs) using Polysulfone (PSF), Polydimethyl Siloxane (PDMS), and zinc oxide (ZnO) nanoparticles. PDMS is a rubbery polymer with exceptional gas permeability, super hydrophobic properties, and excellent mechanical and chemical stability 57,58 . PSF is a glassy polymer that performs well in separating CO 2 59 . ZnO is a common nanoparticle with attractive attributes such as low cost, good chemical, electrical, and mechanical properties, and a high surface-to-volume ratio compared to other nanoparticles 60 . ZnO nanoparticles are also a great option for CO 2 adsorption due to their inherent affinity 61-63 . Theory and simulation procedure. Combination of significant properties of NPs with the natural features of polymers undoubtedly improves the physical and transport properties of novel MMMs 64 . In present article, the gas transport behavior of PSf polymer blended with PDMS, and loaded with ZnO NPs has been investigated It is worth pointing that, solution-diffusion is the dominant mechanism of dense membranes regarding the transport behavior and associated diffusion and solubility coefficients 56,65 . Different parameters such as the interactions of polymer-gas molecules, gas-gas has much of a role to play in altering diffusivity and solubility coefficients. The permeability and selectivity values can be calculated by Eqs. (1) and (2), respectively.
where D is the diffusivity coefficient, S is the solubility coefficient and α A/B is the selectivity of gas A/B 64,66,67 . Generally, the selectivity can be defined as the permeability of one component over the other one which literally indicates the competence of each gas molecules.
Regarding the simulation process, Materials Studio software package from Accerlys Inc version 6.0 and COM-PASS II force field was utilized to construct raw materials and conduct all the simulation steps. GCMC and MD are the two most oftenly utilized methods to determine the solubility and diffusivity coefficients, respectively. Various MMMs were simulated using different weight percent of PSf, PDMS and ZnO NPs. Some analysis like FFV, T g , and XRD have been applied to determine the structural features and properties of the constructed membranes. Adsorption isotherms and Mean Square Displacement (MSD) graphs were additionally utilized to estimate both solubility and diffusivity coefficients, respectively. To this end, the present molecular simulation study (at microscopic level) prognosticated the gas separation properties of all constructed MMMs. MMM construction. The periodic cells were simulated employing PSf and PDMS polymers chain with 10 chain length. Clearly, 10 and 20 wt% of PDMS was blended with PSf polymer to evaluate the effect of polymer blending. Additionally, the simulated cells were cubic in shape and sized between 30-40 Å, depending on the amount of materials loaded. The blended polymers were loaded by 2, 4 and 6 wt% of ZnO NPs. Hence, various MMMs were simulated. The ZnO NP was constructed in a 5 Å cubic form. Figure 1 indicates the periodic cells and raw materials 68 . Constructed materials, polymer chains and NP were also optimized from the energy and geometry perspective. It was chosen for the amorphous module to create 5 output frames; whereas 0.7 g cm −3 (at 298 K) was the selected value for the initial density. Finally, the obtained amorphous cells blended by 10 and 20 wt% of PDMS and dissimilar ZnO loading were acquired. Table 1 indicates the 9 different simulated membranes and their appointed names.
Forcite module was applied to optimize the simulated membranes. The non-equilibrium energy was eliminated by choosing smart method for better convergence. The obtained configurations were considered and the one showing the lowest level of energy was selected. The annealed procedure performing in the range of 298 (1) P A = D A× S A , www.nature.com/scientificreports/ and 500 k at a 5-cycle process was applied in an NPT run. Then, a 4000 ps-NPT run was implemented over the selected configuration to attain the final and experimental density. Additionally, in order to equilibrate the membrane structure with the experimental density, a 1000 ps-NVT run was conducted. Simultaneously, all gas molecules were simulated and then optimized by Forcite module. All the experiments were conducted at 298 K. Additionally, in order to control the temperature at the designated heating temperature and pressure of 1 atm, the simulation utilized the Nose thermostat with a Q ratio of 0.01 and the Berendsen barostat with a decay constant of 0.1 ps. Herein, the COMPASS II force field, along with atom-based electrostatic and van der Waals summation methods were selected with a fine cutoff distance of 12.5 Å. Figure 1 demonstrate the final configurations of optimized MMMs.

Results and discussion
Simulation methods. Fractional  where V w and V s are van de Waals and specific volumes, respectively. It is worth pointing that, the polymer chains' occupied volume is usually 1.3 times greater than their van der Waals volume.
(   Table 2, incorporation of PDMS and ZnO NP into the membrane matrix resulted in higher FFV. Also, 80%PSf + 20%PDMS membrane loaded with 6 wt% ZnO indicated the highest FFV value. Moreover, FFV value increased from 17.1 to 20.8 because of more NP content introduced into the polymer matrix for PSf and 80%PSf + 20%PDMS, respectively. In general run of things, more nanomaterial loading more voids creation between polymer chains which takes place with greater d-spacing values. The special structure of ZnO undoubtedly enhanced the polymer chain distances and caused more fractional volume in polymer matrix. According to the FFV results, the effect of ZnO loading in PSf membrane matrix is obvious which follows an increasing trend starting from 17.01 to 20.1. The resulted FFV data are summarized in Table 2. Glass transition temperature (T g ). T g is a transition temperature that estimates the change in material state from a glassy state to a rubbery state that happens in amorphous polymers. As Fig. 2 indicates, the T g of the constructed MMMs has displayed an increasing trend with ZnO loading. Also, the effect of loading 10 and 20 wt% of PDMS into the PSf polymer matrix is considerable. Which proves the resulted polymers stemming from combination of PSf and PDMS loaded ZnO tend to higher T g values. The glassy temperature of polymer blends can be calculated from Fox equation as below 56,71-76 : Here T g−mix and T g−i are the T g of the mixture/copolymer and of the components, respectively, and ω i is the mass fraction of component i. It was observed that increase in ZnO content made slight changes in T g , which support the suggestion of no evident interaction between PDMS and ZnO NPs. In this subject, this happening can be attributed to the limited movement of the polymer backbone arising from PSF/PDMS-ZnO interactions. Figure 2 shows the calculated T g for all simulated membranes. Fig. 3 presenting the scattering diffraction patterns of the MMM, the maximum peaks are usually considered more significant than other patterns because of the possibility of calculating the d-spacing values based on Bragg's equation d = 2 sinθ . This equation explains the intersegmental distances between polymer back bones 68,77 . By comparing the XRD patterns of simulated membranes, it can be concluded that the main peak of each sample is 2θ = 15°-20° and with increment of ZnO content, the main peak gets sharper and mainly locates in lower 2θ. For instance, the value of 2θ of pure PSf is around

X-ray diffraction (XRD). As can be seen in
The calculated T g of simulated samples. Density. In current molecular simulation study, after selecting the density with initial value of 0.7 g cm −3 , the process of constructing MMMs was applied. Also, Fig. 4 indicates the density graph of 80%PSf + 20%PDMS membranes loaded by 2, 4, and 6 wt% ZnO at 4, 8, 12 and 16 bar. It was observed that, the number of loaded PSf, PDMS chains and the amount of ZnO NPs in the polymer matrix directly effect of the density values of simulated membranes with various and different length as Table 3 summarized the acquired average densities of simulated membranes. It is noteworthy that, NPT runs have been applied to attain the actual density of each system which definitely modifies the density and dimensions of each cell. Consequently, the density of cells started to increase by a considerable reduction in cell length. Figure 4 indicates that the membrane density increased along with run time, whereas after 2000 ps a plateau was reached for the rest of the operating time. Therefore, the adequacy of the 4000 ps-NPT run was confirmed for reaching the equilibrium state.  Based on Eq. (5), CO 2 , N 2 and CH 4 gases start penetrating within the membrane relying on the diffusion mechanism happening in a pico-second. It is worth to note that, this motion relation is proportional to t x function when the initial condition (x < 1) applies 79 . To calculate D i of all gases in simple PSf and all MMMs, three different gas molecules (CO 2 , N 2 , CH 4 ) with optimized geometries and minimized energies were inserted into the simulated membrane. The final configurations indicated the minimum energy. Then, the MSD results were evaluated and consequently the D i was calculated. These data were the results of three consecutive experiments as an average which were reported in Table 4. By taking a look at Table 4, it becomes obvious that the D i of gas molecules within the constructed membranes increases by higher loading of ZnO stemming from higher FFV and more free paths for gas diffusion. The same trend was observed for loading 10 and then 20 wt% of PDMS. To make sure that the MD simulation results are reliable, Fig. 5 revealed that the slope of Log (MSD) vs. Log (time) tend to reach unit 80 . As can be seen in this figure, the amount of MSD for CO 2 gas is higher than N 2 and CH 4 , respectively, because of the linear structure of this gas which accelerates and increases the transfer diffusion through the MMMs compare to methane, which has a Tetrahedron structure.
Solubility coefficients. To calculate the solubility coefficient of each gas molecules within the simulated simple PSf and MMMs, GCMC was hired including the Metropolis method as a reliable task in Sorption module. Besides, adsorption isotherms is another task that can evaluate the effect of some experimental condition such as pressure and temperature on the solubility coefficient. Additionally, one of the other advantages of GCMC method is reaching to a better understanding of the sorption mechanism at the atomistic level. This sorption mechanism can be included some values such as regrowth, conformer rotation, translation and exchange. Notwithstanding, the Metropolis task involves a number of moves just like translation, rotation and exchange. Equation (6) indicates the acceptance probability as follows: Generally, GCMC method works based on the trial insertion and deletion of molecules, in which, 10 5 equilibrium steps and 10 6 production steps 44 were set to conduct the adsorption isotherm calculations. Equation (7) shows the probability of rejecting or accepting a new location for any gas as follows: where E , f i ,N i , and V can be defined as the difference of Van der Waals interaction and columbic interaction for two configurations, the fugacity, the number of molecules for component i, and the volume of amorphous cell, respectively 68,83 . To measure the solubility coefficient, the slope of adsorption isotherms represents was measured as Eq. (8) indicates 65,84 : where P is the fugacity and C represents the gas concentration. Figure 6 indicates the adsorption isotherm diagrams for all diffusing molecules across the simulated membranes.
Generally, various factors can directly affect on gas permeation such as FFV, crystallinity, pressure, temperature, and so on. In current simulation study, the structural features and separation properties of constructed membranes have been affected by different factors from different aspects. Inevitably, some of them had negative impact on gas separation performance while some others positively enhanced its performance. Therefore, the summation of all these positive and negative effects lead to a certain value for gas permeability. So, evaluating all these factors can be of great help to reach a better understand of the system.
As it is obvious in Table 5, CO 2 solubility within the membranes is much greater than CH 4 and N 2 . The main reason may be attributed to the fact that CO 2 is an acid gas and PSf shows better affiliation with CO 2 . Also, Table 5 shows that, the solubility coefficients of pure gases through the membranes generally enhance with more ZnO content, which indicates the effect of presence of ZnO NPs in polymer matrix. Also, these figures experience an upward trend when the PDMS content increases. Although, the T g experiences a slight increase, higher solubility coefficients convey this meaning that the membranes confronted with expanded amorphous region which provided the polymer matrix with a higher chance of adsorbing more gas molecules. To clarify, the increasing trend of measured slopes regarding the adsorption isotherms proves the gradual increase of the solubility coefficients of utilized gas molecules. On the other side, the acquired results of MSD analysis revealed that the diffusivity coefficients of each gas molecules experienced a gradual increase due to the presence of PDMS polymer chains  www.nature.com/scientificreports/ and more pore and channels of created by ZnO NPs. According to the conducted experiments, the results of gas permeability have been evaluated exhaustively in the next section.

Gas permeability and perm-selectivity
In general, the permeability can be explained as the multiplication of solubility and diffusivity coefficients. In this section, the permeability of three pure gas molecules were calculated to thoroughly investigate the performance of simulated membranes. In this regard, two loadings of PDMS and 4 different loading of ZnO NPs have been incorporated into the PSf matrix. So, it can be perceived that NPs loading is another influential factor affecting the gas permeability. Notably, as mentioned before all raw materials have been optimized geometrically and minimized in aspect of energy level. Also, all simulation practices were performed at thermodynamic equilibrium state. A 1000-ps NVT and 4000-ps NPT MD runs were conducted to eliminate the non-equilibrium states and reach the final density. It should be noted that, Nose-Hoover thermostat was chosen as the temperature controller these MD runs.
All three gas molecules were inserted into the simulated MMM to measure the D i . This coefficient can be calculated as the slope of MSD graph. The reason that validates the obtained results is that the slope of Log (MSD) vs. Log (time) diagram for all gases unify 85 . On the other side, having used the GCMC method, the solubility coefficients of all gas molecules were computed. Figure 7 illustrates the effect of ZnO loading on gas permeability through simple PSf membrane.
As can be seen from Fig. 7, CO 2 showed the highest permeability over two other gases. CH 4 permeability is considerably greater than N 2 permeability. Besides, it is obvious that, loading more ZnO content led to greater permeabilities of all gasses. The other simulated MMMs were tested by gas permeability and the effect of ZnO loading and PDMS blending were considered. Figure 8 indicates clearly the effect of these parameters. A brief  www.nature.com/scientificreports/  www.nature.com/scientificreports/ look at Fig. 8 indicates that adding more ZnO content due to providing higher d-spacing and expanded distances between polymer chains generally leads to higher permeability values. Although, the effect of NPs is considerable, in some cases loading 6 wt% of ZnO resulted in lower permeability compare to 4 wt% which may stem from agglomeration of NPs playing a negative role against permeability. Additionally, by applying more operational pressure (4, 8, 12, and 16 bar), permeability of all three gases increases 71 . On the other side, the perm-selectivity of membranes are listed in Table 6. It is clear that ZnO loading negatively effects on CO 2 /CH 4 selectivity, while PDMS blending increases its selectivity. Besides, CO 2/ N 2 selectivity followed the same trend in both ZnO loading and PDMS blending. The before mentioned trends can be attributed to the ZnO nature and structure which tends to let all the three gases pass freely within the membrane. Also, the PDMS blending enhanced the MMMs performance resulted in better gas separation. The increasing feed pressure was considered as a positive effect on perm-selectivity which moderately changed their performance. The results obtained from simulation study were compared with the experiments for the perm-selectivity within PSF/PDMS composite membrane, without ZnO NPs 86 . It was concluded that both simulation and experimental results are in good agreement.

Comparison with the literature
The effectiveness of MMMs for technical uses is determined by two primary factors: selectivity and permeability. In this study, the selectivity of gas pairs was compared to outcomes from earlier research and the compiled information is listed in Table 7 with corresponding references. The results indicate that the MMMs developed in this investigation have superior selectivity values for CO 2 /CH 4 and CO 2 /N 2 separation compared to previously studied membranes. The PSf/PDMS-Nano ZnO MMM exhibited significant potential for industrial applications such as natural gas sweetening or biogas purification and warrants further exploration.

Robeson's upper bound
The gas separation performance of simulated periodic cells were examined by Robeson's upper bound 14 which is plotted for the selectivity vs. permeability of gas pairs of N 2 , CH 4 , and CO 2 . This plot indicates the acquired data based on the selectivity vs. permeability of the simulated membranes. What perceived from this plot is that which membranes demonstrated more appropriate separation performance compare to the industry standards 68,56 . In Table 6. The effect of feed pressure, ZnO loading and PDMS blending on gas perm-selectivity. *The experimental value reported in the literature 86  www.nature.com/scientificreports/ other words, closer points to the Robeson's upper bound proclaim that those points associated with membrane have better separation performance. Figure 9 indicates the Robeson's Upper Bound for CO 2 /CH 4 and CO 2 /N 2 at 4 and 16 bar. A brief look at the Fig. 9 shows that the simulated membranes had better CO 2 /N 2 separation performance than CO 2 /CH 4 . This result is attributed to the fact that, CH 4 showed double as the N 2 permeability. Moreover, the membranes loaded by 4% wt% of ZnO had better performance than others in which 20 wt% PDMS blended membrane were moderately better than 10 wt. % blended ones.

Conclusion
The permeability of some pure gas molecules (e.g., CO 2 , N 2 and CH 4 ) within sveral suggested MMMs were predicted using molecular simulation methods. In this regard, Psf polymer matrix was loaded by various content of ZnO NPs and blended 10 and 20 wt% of PDMS. Also, their performance was evaluated using MS by some structural and transport analysis. T g and FFV results illustrated that the loading ZnO NPs directly influenced the membrane matrix, which led to different gas permeability. Blending 10 and then 20 wt% PDMS clearly improved the membrane performance. In other words, higher perm-selectivity was achieved by more blended polymer. ZnO loading resulted in higher T g and more rigid sections. However, it improved the FFV values. It was shown that the more pressure applied, the more permeability and selectivity values resulted. The T g of the simulated MMMs experienced an increasing trend with increasing ZnO content, indicating that MMMs had more extended rigid region than unfilled membranes. The fact that the slopes of adsorption isotherms experienced an increasing trend proved that that the solubility coefficients of employed gas molecules soared gradually. With reference to the MSD analysis, it was obvious that D i of gas molecules changed gently because of higher pore and channels, higher pressure, the ZnO content. In conclusion, this simulation study reveals that, the PSf/ PDMS polymer matrix membrane incorporated with ZnO NPs might be a fascinating MMM for separation of CO 2 /CH 4 /N 2 mixtures in gas refineries plants.
The transferability of a simulation method used in a study to other mixed matrix membranes for gas separation depends on several factors, such as the molecular interactions between the gas molecules and the membrane material, as well as the structural properties of the membrane. In general, the transferability of a simulation www.nature.com/scientificreports/ method can be improved if the method has been validated using experimental data and if it accounts for the specific properties of the membrane material, such as pore size, surface area, and surface chemistry. Additionally, the simulation method should be able to capture the dynamic behavior of the gas molecules within the membrane, including adsorption and desorption processes, as well as diffusion and transport. However, it is important to note that even with a well-validated simulation method, the transferability of the results to other mixed matrix membranes may be limited due to the differences in the composition and structure of the membranes. Therefore, it is recommended to validate the simulation method for each specific membrane material and to account for any differences in the properties of the membrane when interpreting the results. Therefore, the results obtained in current article have been compared with experimental results as discussed in previous sections. Finally, MS can be considered as a prospective and profitable tool to not only estimate the structural features and separation properties of polymeric structures but also to optimize the operating factors which undoubtedly enhance the membrane separation performance relying on their promising features.

Data availability
All data generated or analysed during this study are included in this published article.